Added a routine to simulate a backward looking stochastic model with arbitrary...

Added a routine to simulate a backward looking stochastic model with arbitrary precision (needed for PEA).

matlab/simul_backward_nonlinear_model.m

+function DynareOutput = simul_backward_nonlinear_model(sample_size,DynareOptions,DynareModel,DynareOutput)
+
+%@info:
+%! @deftypefn {Function File} {@var{DynareOutput} =} simul_backward_nonlinear_model (@var{sample_size},@var{DynareOptions}, @var{DynareModel}, @var{DynareOutput})
+%! @anchor{@simul_backward_nonlinear_model}
+%! @sp 1
+%! Simulates a stochastic non linear backward looking model with arbitrary precision (a deterministic solver is used).
+%! @sp 2
+%! @strong{Inputs}
+%! @sp 1
+%! @table @ @var
+%! @item sample_size
+%! Scalar integer, size of the sample to be generated.
+%! @item DynareOptions
+%! Matlab/Octave structure (Options used by Dynare).
+%! @item DynareDynareModel
+%! Matlab/Octave structure (Description of the model).
+%! @item DynareOutput
+%! Matlab/Octave structure (Results reported by Dynare).
+%! @end table
+%! @sp 1
+%! @strong{Outputs}
+%! @sp 1
+%! @table @ @var
+%! @item DynareOutput
+%! Matlab/Octave structure (Results reported by Dynare).
+%! @end table
+%! @sp 2
+%! @strong{This function is called by:}
+%! @sp 2
+%! @strong{This function calls:}
+%! @ref{dynTime}
+%!
+%! @end deftypefn
+%@eod:
+
+% Copyright (C) 2012 Dynare Team
+% stephane DOT adjemian AT univ DASH lemans DOT fr
+%
+% This file is part of Dynare.
+%
+% Dynare is free software: you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation, either version 3 of the License, or
+% (at your option) any later version.
+%
+% Dynare is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with Dynare.  If not, see <http://www.gnu.org/licenses/>.
+
+if DynareModel.maximum_lead
+    error(['simul_backward_nonlinear_model:: The specified model is not backward looking!'])
+end
+
+% Set the covariance matrix of the structural innovations.
+variances = diag(DynareModel.Sigma_e);
+number_of_shocks = length(DynareModel.Sigma_e);
+positive_var_indx = find(variances>0);
+effective_number_of_shocks = length(positive_var_indx);
+covariance_matrix = DynareModel.Sigma_e(positive_var_indx,positive_var_indx);
+covariance_matrix_upper_cholesky = chol(covariance_matrix);
+
+% Set seed to its default state.
+if DynareOptions.bnlms.set_dynare_seed_to_default
+    set_dynare_seed('default');
+end
+
+% Simulate structural innovations.
+switch DynareOptions.bnlms.innovation_distribution
+  case 'gaussian'
+      DynareOutput.bnlms.shocks = randn(sample_size,effective_number_of_shocks)*covariance_matrix_upper_cholesky;
+  otherwise
+    error(['simul_backward_nonlinear_model:: ' DynareOption.bnlms.innovation_distribution ' distribution for the structural innovations is not (yet) implemented!'])
+end
+
+% Put the simulated innovations in DynareOutput.exo_simul.
+DynareOutput.exo_simul = zeros(sample_size,number_of_shocks);
+DynareOutput.exo_simul(:,positive_var_indx) = DynareOutput.bnlms.shocks;
+DynareOutput.exo_simul = [zeros(1,number_of_shocks); DynareOutput.exo_simul];
+
+% Get usefull vector of indices.
+ny0 = nnz(DynareModel.lead_lag_incidence(2,:));
+ny1 = nnz(DynareModel.lead_lag_incidence(1,:));
+iy1 = find(DynareModel.lead_lag_incidence(1,:)>0);
+idx = 1:DynareModel.endo_nbr;
+jdx = idx+ny1;
+hdx = 1:ny1;
+
+% Get the name of the dynamic model routine.
+model_dynamic = str2func([DynareModel.fname,'_dynamic']);
+
+% initialization of vector y.
+y = NaN(length(idx)+ny1,1);
+
+% initialization of the returned simulations.
+DynareOutput.endo_simul = NaN(DynareModel.endo_nbr,sample_size+1);
+DynareOutput.endo_simul(:,1) = DynareOutput.steady_state;
+
+% Simulations (call a Newton-like algorithm for each period).
+for it = 2:sample_size+1
+    y(jdx) = DynareOutput.endo_simul(:,it-1); % A good guess for the initial conditions is the previous values for the endogenous variables.
+    y(hdx) = y(jdx(iy1));                     % Set lagged variables.
+    y(jdx) = solve1(model_dynamic, y, idx, jdx, 1, 1, DynareOutput.exo_simul, DynareModel.params, DynareOutput.steady_state, it);
+    DynareOutput.endo_simul(:,it) = y(jdx);
+end
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